Comparing Rational Numbers: TEAS Practice Question with Answer & Explanation

Deciphering the Greatest Value

To determine the greatest value among a mix of decimals and fractions, the most efficient strategy for the TEAS Math section is to convert all values into the same format, typically decimals. Decimals allow for a direct digit-by-digit comparison from left to right.

Step-by-Step Conversion

1. Value A: 2.65

   • This is already in decimal form.

2. Value B: ⁸⁄₃ (8 divided by 3)

   • Perform long division: 8 ÷ 3 = 2.666... (repeating).
   • To make comparison easier, we can round this to 2.667.

3. Value C: 2.607

   • This is already in decimal form. Note that while it has more digits than 2.65, the value depends on the place value, not the length of the number.

4. Value D: ¹³/₅ (13 divided by 5)

   • Perform long division: 13 ÷ 5 = 2.6.
   • To keep place values consistent, we can view this as 2.600.

Comparing the Results

Now that we have all four values in decimal form, we align them by the decimal point and compare from left to right (Units → Tenths → Hundredths):

• A) 2.650
• B) 2.667
• C) 2.607
• D) 2.600

While all values begin with "2.6," the hundredths place reveals the winner. Value B has a "6" in the hundredths place, which is greater than the "5" in Value A and the "0" in Values C and D. Therefore, ⁸⁄₃ is the greatest value.

Why the Other Choices Are Incorrect

• Choice A (2.65) is less than 2.667. Students often pick this if they round the fraction incorrectly.
• Choice C (2.607) is the smallest "thousandth" value. It is easy to mistake this as "large" because it has many digits, but the zero in the hundredths place makes it smaller than 2.65.
• Choice D (¹³/₅) equals exactly 2.6. This is smaller than both 2.65 and 2.667.

TEAS Concept: Rational Number Comparison

The TEAS exam expects you to fluently move between fractions, decimals, and percentages. Always convert to decimals first—it is the most reliable way to avoid "visual tricks" where a fraction looks larger just because the denominator is a certain number.

Memory Tip

When comparing decimals, "Fill with Frills" (Zeros). Add trailing zeros so every number has the same amount of digits after the decimal (e.g., changing 2.6 to 2.600). This makes it much harder to accidentally think 2.607 is larger than 2.65.